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on Game Theory |
| By: | Carmona, Guilherme |
| Abstract: | Over the years, several formalizations of games with a continuum of players have been given. These include those of Schmeidler (1973), Mas-Colell (1984) and Khan and Sun (1999). Unlike the others, Khan and Sun (1999) also addressed the equilibrium problem of large ¯- nite games, establishing the existence of a pure strategy approximate equilibrium in su±ciently large games. This ability for their formal- ization to yield asymptotic results led them to argue for it as the right approach to games with a continuum of players. We challenge this view by establishing an equivalent asymptotic theorem based only on Mas-Colell's formalization. Furthermore, we show that it is equivalent to Mas-Colell's existence theorem. Thus, in contrast to Khan and Sun (1999), we conclude that Mas-Colell's for- malization is as good as theirs for the development of the equilibrium theory of large ¯nite games. |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:unl:unlfep:wp487&r=gth |
| By: | Carmona, Guilherme |
| Abstract: | Radzik (1991) showed that two-player games on compact intervals of the real line have " { equilibria for all " > 0, provided that payo® functions are upper semicontinuous and strongly quasi-concave. In an attempt to generalize this theorem, Ziad (1997) stated that the same is true for n-player games on compact, convex subsets of Rm, m ¸ 1 provided that we strengthen the upper semicontinuity condition. We show that: 1. the action spaces need to be polyhedral in order for Ziad's ap- proach to work, 2. Ziad's strong upper semicontinuity condition is equivalent to some form of quasi-polyhedral concavity of players' value func- tions in simple games, and 3. Radzik's Theorem is a corollary of (the corrected) Ziad's result. |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:unl:unlfep:wp488&r=gth |
| By: | Carmona, Guilherme |
| Abstract: | We present a puri¯cation result for incomplete information games with a large ¯nite number of players that allows for compact metric spaces of actions and types. This result is then used to generalize the puri¯cation theorems of Schmeidler (1973), Rashid (1983) and Kalai (2004). Our proofs are elementary and rely on the Shapley-Folkman theorem. |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:unl:unlfep:wp491&r=gth |
| By: | Yair Tauman; Andriy Zapechelnyuk |
| Abstract: | We consider a bargaining problem where one of the players, the bureaucrat, has the power to dictate any outcome in a given set. The other players, the agents, negotiate with him which outcome to be dictated. In return, the agents transfer some part of their payoffs to the bureaucrat. We state ?five axioms and characterize the solutions which satisfy these axioms on a class of problems which includes as a subset all submodular bargaining problems. Every solution is characterized by a number <FONT FACE="Symbol">a</FONT> in the unit interval. Each agent in every bargaining problem obtains a weighted average of his individually rational level and his marginal contribution to the set of all players, where the weights are <FONT FACE="Symbol">a</FONT> and 1 - <FONT FACE="Symbol">a</FONT>, respectively. The bureaucrat obtains the remaing surplus. The solution when <FONT FACE="Symbol">a</FONT> = 1/2 is the nucleolus of a naturally related game in characteristic form. |
| Date: | 2006–06 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp425&r=gth |
| By: | Carmona, Guilherme |
| Abstract: | We consider anonymous games with a Lebesgue space of players in which either the action space or players' characteristics are denumer- able. Our main result shows that the set of equilibrium distributions over actions coincides with the set of distributions induced by equilib- rium strategies. This result, together with Mas-Colell (1984)'s theorem, implies that any continuous, denumerable game has an equilibrium strategy. In particular, the theorems of Khan and Sun (1995) and Khan, Rath, and Sun (1997) can be obtained as corollaries of Mas-Colell's. |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:unl:unlfep:wp485&r=gth |
| By: | Uwe Dulleck (Department of Economics, Johannes Kepler University Linz, Austria); Paul Frijters (Queensland University of Technology); Konrad Podczeck (University of Vienna) |
| Abstract: | We study all-pay auctions with budget-constrained bidders who have access to fair insurance before bidding simultaneously over a prize. We characterize a unique equilibrium for the special cases of two bidders and one prize, show existence and a heuristic for finding an equilibrium in the case of multiple bidders and multiple prizes. We end with an example of non-uniqueness of equilibria for the general case of multiple prizes and multiple players. |
| Keywords: | all-pay auctions; fair lotteries; political campaigning; oligopoly; regional competition; patent races |
| JEL: | C72 D72 D42 |
| Date: | 2006–07 |
| URL: | http://d.repec.org/n?u=RePEc:jku:econwp:2006_13&r=gth |
| By: | Carmona, Guilherme; Fajardo, Jose |
| Abstract: | We establish the existence of sequential equilibria in general menu games, known to be su±cient to analyze common agency problems. In particular, we show that our result solves some unpleasant features of early approaches. |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:unl:unlfep:wp490&r=gth |
| By: | Carmona, Guilherme |
| Abstract: | We present two simple proofs of existence of subgame perfect equi- libria in continuous games with perfect information. |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:unl:unlfep:wp486&r=gth |
| By: | Carmona, Guilherme |
| Abstract: | We consider a two-player game in which one player can take a costly action (i.e., to provide a favor) that is bene¯cial to the other. The game is in¯nitely repeated and each player is equally likely to be the one who can provide the favor in each period. In this context, equality matching is de¯ned as a strategy in which each player counts the number of times she has given in excess of received and she gives if and only if this number has not reached an upper bound. We show that the equality matching strategy is simple, self-enforcing, symmetric, and irreducible. Furthermore, we show that the utility for each player is at least as high under equality matching as under any other simple, self-enforcing, symmetric, and irreducible strategy of the same complexity. Thus, we rationalize equality matching as being an e±cient way to achieve those properties. This result is applied to risk sharing in village economies and used to rationalize the observed correlations between individual consump- tion and individual income and between present and past transfers across individuals. |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:unl:unlfep:wp489&r=gth |
| By: | Alexander Matros; Andriy Zapechelnyuk |
| Abstract: | We consider a multi-period auction with a seller who has a single object for sale, a large population of potential buyers, and a mediator of the trade. The seller and every buyer have independent private values of the object. The mediator designs an auction mechanism which maximizes her revenue subject to certain constraints for the traders. In each period the seller auctions the object to a set of buyers drawn at random from the population. The seller can re-auction the object (infinitely many times) if it is not sold in previous interactions. We characterize the class of mediator-optimal auction mechanisms. One of such mechanisms is a Vickrey auction with a reserve price where the seller pays to the mediator a fixed percentage from the closing price. |
| Date: | 2006–06 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp424&r=gth |
| By: | A. Batabyal |
| Abstract: | I describe the theoretical and empirical contributions that rigorous economic analysis can make in improving our understanding of the causes of and the solutions to a variety of international environmental problems. I do this by analyzing and summarizing the intellectual contributions of fourteen papers about the design and the implementation of international environmental agreements (IEAs). |
| Keywords: | Economic theory, game theory, international environmental agreement |
| JEL: | Q20 F42 |
| URL: | http://d.repec.org/n?u=RePEc:usu:wpaper:2000-02&r=gth |